A particle of mass m and charge q is moving in a region where uniform, constant electric and mangetic fields `vec E and vec B` are present. `vec E and vec B` are parallel to each other. At time `t=0,` the velocity `vec v_0` of the particle is perpendicular to `vec E` (Assume that its speed is always `lt lt c`, the speed of light in vacuum). Find the velocity `vec v` of the particle at time `t`. You must express your answer in terms of `t, q, m,` the vector `vec v_0, vec E` and `vec B` and their magnitudes `vec v_0, vec E` and `vec B`.

Explanation

To find the velocity \(\vec{v}\) of a particle of mass \(m\) and charge \(q\) moving in uniform electric field \(\vec{E}\) and magnetic field \(\vec{B}\) that are parallel to each other, we can follow these steps:

### Step 1: Understand the Forces Acting on the Particle
The particle experiences two forces:
1. **Electric Force**: \(\vec{F}_E = q \vec{E}\)
2. **Magnetic Force**: \(\vec{F}_B = q \vec{v} \times \vec{B}\)

### Step 2: Set Up the Initial Conditions
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